Grade 8 · Math

8th grade Solve a system by adding or subtracting the equations worksheet

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Solve a system by adding or subtracting the equations

Grade 8 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Zee multiplies 2x + y = 7 by 2, then adds it to 3x - 2y = 7. What is the solution (x, y)?
To solve x + y = 11 and -x - 2y = -15, Noah first multiplies x + y = 11 by 2, then adds. What is the solution (x, y)?
Tala plans it out: multiply -x + y = -4 by 3, then add 4x - 3y = 17. A neat plan! What is the solution (x, y)?
Ren multiplies x + y = 2 by 3 so the y terms become opposites in x - 3y = -14. What is the solution (x, y)?
5.
Esme tries elimination on 2x + 3y = 6 and 4x + 6y = 9, multiplying one equation first. How many solutions does the system have?
- no solution
- infinitely many solutions
- exactly one solution
6.
Bo finds x - 2y = 3 and 3x - 6y = 4 in a puzzle book with a page missing. How many solutions does the system have?
- exactly one solution
- no solution
- infinitely many solutions
7.
Milo tries elimination on x - 3y = 2 and 3x - 9y = 6, multiplying one equation first. How many solutions does the system have?
- no solution
- exactly one solution
- infinitely many solutions
8.
Pia finds 2x + y = 5 and 6x + 3y = 15 in a puzzle book with a page missing. How many solutions does the system have?
- infinitely many solutions
- exactly one solution
- no solution
Kira measures two sunflowers, x cm and y cm tall: x + y = 250 and x - y = 30. What point (taller cm, shorter cm) solves the system?
Milo reads a mystery book (x pages) and a comic (y pages): x + y = 300 and x - y = 120. What point (mystery, comic) solves the system?

Solve a system by adding or subtracting the equations. Every version has 10 questions, and the answer key prints on the second page.

I can add two equations when their y terms are opposites, or subtract them when the y terms are equal, and solve for the shared point (x, y).
I can multiply a whole equation, both sides, so that a letter will cancel.
I can read the last line: false (0 = 6) means no solution, true (0 = 0) means infinitely many, and a letter equal to 0 is one solution.

Standard: 8.EE.C.8b (algebraic)

system of equations: Two equations about the same x and y, worked on together.

solution: An (x, y) that makes both equations true: the point both lines share.

eliminate: Make one letter cancel out by adding or subtracting the equations.

opposite terms: Terms like 3y and −3y that add to 0.

multiply an equation: Multiply every term on both sides by the same number.

Your child found where the two lines meet but wrote the point backward, with the up number first.

Your child found where the two lines meet but gave only the first number, not the whole point.

Your child combined the two equations but lost a minus sign, so a letter that should cancel stayed in.

Ask: which number goes across, and which goes up?

Ask: at that spot, how high are the lines?

Ask: what is 3y take away 3y?

What is the most common mistake with solve a system by adding or subtracting the equations?

Your child found where the two lines meet but wrote the point backward, with the up number first.

How can I help my child with solve a system by adding or subtracting the equations?

Ask: which number goes across, and which goes up?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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